The rise in energy of frequency-drift lasers, of titanium-doped sapphire type, is leading to the appearance of problems regarding control of the spectrum, and therefore pulse duration, in high-energy amplifiers.
Indeed, in this type of amplifier, the signal level is for example close to saturation, thus giving rise to deformations of the amplified spectrum, and therefore limiting the performance in terms of pulse duration.
A conventional solution consists in pre-compensating, at the start of the chain, for the spectral deformation. This filtering-based solution is naturally penalizing in terms of efficiency, since it acts by filtering, and therefore causes energy losses.
Frequency-drift technology is based on the use of a wide spectrum, pulse stretching, amplification and re-compression.
Typically, Ti:Sa chains have an oscillator spectrum of from 5 to 100 nm, for compressed pulse durations of from 150 to 10 fs approximately. The ability of the amplification chain to maintain a correct spectrum directly influences the ability of the laser to work with short pulses.
The spectral constriction induced by the amplifiers is therefore a key factor for obtaining short-duration performance. Likewise, a large deformation of the spectrum, for example asymmetric, disturbs the temporal shape and impairs the operation of the laser.
The amplifiers used are of the type with n passes (2 to 4 conventionally, but configurations with more passes exist) of the beam through the crystal, the amplifying medium.
The pump laser dispatches a pulse into the crystal and the beam to be amplified is thereafter dispatched and performs n passes so as to optimize the extraction in terms of energy.
FIG. 1 diagrammatically depicts a multi-pass amplifier of this kind, which essentially comprises a crystal CR (for example Ti:Sa) receiving, from an input mirror ME, input pulses at an angle differing from the normal to its incidence surface, and several reflecting mirrors M1 to M7 disposed on either side of the crystal 1 so as to cause the beam to pass through the crystal at various angles of incidence, the last mirror M7 reflecting this beam to the output via an output mirror MS.
The gain of the amplifier may be written:
      E    OUT    =            J      SAT        ·    S    ·          ln      ⁡              (                                                            J                STO                                            J                SAT                                      ⁢                          (                                                e                                                            E                      in                                                              SJ                      SAT                                                                      -                1                            )                                +          1                )            
JSTO being the stored fluence available for the gain in the medium, JSAT the saturation fluence of this medium and S the pumped laser crystal surface area. This is the classical equation from the theory of Frantz and Nodvick.
The table below contains a few examples of values of JSAT for various laser materials:
MaterialsJsat in J/cm2Spectral rangeDyes~0.001J/cm2VisibleExcimers~0.001J/cm2UVNd:YAG0.5J/cm21064 nm Ti:Al2O31.1J/cm2800 nmNd:Glass5J/cm21054 nm Alexandrite22J/cm2750 nmCr:LiSAF5J/cm2830 nm
In the small-signal regime, with JIN<<JSAT, the gain relation can be approximated with:
  G  =                    E        OUT                    E        IN              =          e              (                              J            STO                                J            SAT                          )            
The shape of the gain curve of the above-described amplifiers being close to a Gaussian, at each pass through the medium, a constriction of the spectrum due simply to the gain is observed.
The curve of FIG. 2 shows a typical exemplary gain in a Ti:Sa crystal as a function of wavelength, this curve being centered on the wavelength of 800 nm.
As a result of the amplification in this medium, a gain which is non-uniform as a function of wavelength will be applied to an input signal of limited spectrum, the effect of which is to cause an alteration: spectral constriction. The example of FIG. 3 illustrates this effect, which is accentuated with the number of passes through the amplifier. The curve of the input signal as a function of its wavelength and the curves of the signal after 1, 4 and 8 passes through the crystal, respectively, have been represented in this FIG. 3.
The graph of FIG. 4 shows the deviation between the single-pass gain and the gain in four passes and reveals the spectrum constriction effect.
It will be noted that when the input signal possesses a spectrum that is non-centered with respect to the maximum of gain of the medium, the spectral constriction is accompanied by a shift effect which tends to return the signal to the maximum gain spike. The graph of FIG. 5 shows a signal centered at 750 nm shifted progressively towards 800 nm during the multi-pass amplification (for 1, 4 and 8 passes, respectively).
To compensate for this effect, a pre-distortion is usable by active or passive filtering at the price of a decrease in the efficiency of the laser. Specifically, the filters used have efficiencies of the order of 50% since they act (cut off) spectrally at the energy maximum.
The amplified pulse being stretched (dispersed), usually positively, the Applicant has highlighted the following problem, described below with reference to FIGS. 6 to 12.
Specifically, chains based on short pulses use a wide-spectrum oscillator and these short pulses are stretched temporally and are thereafter amplified and re-compressed at the output. Such a chain is schematically represented in FIG. 6, this chain essentially comprising an oscillator 1, a stretcher 2, one or more amplification stages 3 and a compression device 4. An exemplary spectrum of a Ti:Sa oscillator signal has been represented in FIG. 7. In this FIG. 7, the spectral phase has been represented as a continuous line.
When the pulse penetrates an amplifier 5, the initial spectral components see a gain g1 and are amplified. The following components being in the amplifier therefore see a gain g2 which has decreased because the start of the pulse has “consumed” stored energy. This temporal action of the gain is shown diagrammatically in FIG. 8.
There is an initial gain for the first temporal part of the form:
  gi  =            j      STO              j      SAT      
and a final gain, which takes account of the extracted energy, of the form:
  gf  =                    j        STI            -              J        ex                    j      SAT      
Jex being the amplifier extracted fluence.
The apparent gain is therefore higher for the temporal start of the signal than for the end, thereby inducing a spectral deformation of the amplified signal.
The curve of FIG. 9 shows the effect of modifying the gain of a laser crystal due to the temporal stretching of the pulses to be amplified. This curve gives the value of the relative gain (in arbitrary units, as is the case for all the other gain curves) as a function of the wavelength of the amplified signal.
FIG. 10 shows two curves of the shift of the gain due to temporal stretching as a function of wavelength, respectively for one pass and for four passes through the crystal.
In addition to the constriction due to the gain, a shift of the spectrum towards the wavelengths extracted first (here, the highest) is observed, as represented in FIG. 11.
It will be noted moreover that, when the input signal is off-centered with respect to the gain of the laser medium, the shift effect is accentuated. Thus, for example, as represented in FIG. 12, the input signal is centered at 760 nm, although after 24 passes through the laser medium, the final signal is centered at 820 nm, the shift increasing in tandem with the successive passes through the laser medium.
The combination of these two effects therefore greatly limits the performance of frequency-drift chains since it limits the re-compression of the incident pulses with a view to obtaining at the output pulses of very short durations.